Abstract

We introduce a stochastic Galerkin mixed formulation of the
steady-state diffusion equation and focus on the efficient iterative solution of the saddle-point systems obtained by combining standard finite element discretisations with two distinct types of stochastic basis functions. So-called mean-based preconditioners, based on fast solvers for scalar diffusion problems, are introduced for use
with the minimum residual method. We derive eigenvalue bounds for the preconditioned system matrices and report
on the efficiency of the chosen preconditioning schemes with respect to all the discretisation parameters